Cooperative binding systems are being studied taking into account site or submit interactions, ligand interactions, aggregation and redistribution in proteins and model systems. Methods have been developed to evaluate reasonable parameters describing these systems, particularly those involving protein-DNA interactions and the helix-coil transition. These phenomena involve large numbers of sites or subunits and analyses so far have been approximations assuming an infinite number of sites. We have developed an exact combinatorial approach for this problem. Our formalism analyzes both small and large numbers of sites and requires only reasonable times on the present high-speed computers. Under analysis at present is the helix-coil transition in polypeptides.